In a machine tool provided with two spindles, it is known to rotate the spindles at the same speed. For example, in a lathe of this kind, two spindles are rotated at the same speed when a shift is made from a state where one end of a workpiece is gripped by a first chuck coupled to one of the spindles, to a state where the other end of the workpiece is gripped by a second chuck coupled to the other spindle. When a workpiece having an anisotropic configuration with respect to the axis thereof is gripped by the second chuck, the workpiece can collide with the second chuck, if the rotational phases (rotational angle positions) of the chucks are different from each other, even though these chucks are rotated at the same speed. In this case, the workpiece can be damaged or deformed.